I had installed a 11.2.0.2 RAC setup few days back with incorrect timezone. It had to be PDT but I installed with UTC.
Starting/stopping clusteware with correct timezone didn’t solve the issue.

In 11.2.0.2 Oracle stores timezone information in file $GRID_HOME/crs/install/s_config_(hostname).txt. In my case file looked like this

cd /oragrid/product/11.2/crs/install
cat s_crsconfig_prod1.txt
<strong>TZ=UTC</strong>
NLS_LANG=AMERICAN_AMERICA.AL32UTF8
TNS_ADMIN=
ORACLE_BASE=

To resolve the issue we need to change TZ to US/Pacific on all nodes and restart clusterware. So entry would be like

<strong>TZ=US/Pacific</strong>

On Restarting clusteware , database and clusteware starts with correct timezone.

In case you wish to have different database timezone only for Oracle database, then it is possible using srvctl command. E.g

srvctl setenv database -d orcl -t TZ=US/Pacific

You can confirm this with getenv command

[oracle@prod1]~% srvctl getenv database -d orcl
orcl:
TZ=US/Pacific

This would require database bounce. Also note that in case database is started manually it would not start with correct timezone. To unset the parameter use following command

[oracle@prod1]~% srvctl unsetenv database -d orcl -t TZ
[oracle@prod1]~% srvctl getenv database -d orcl
orcl:

Hope this helps